In a reciprocating piston compressor of the named type known from the Baumann U.S. Pat. No. 5,033,940 the piston and the cylinder are each executed with a running surface of an abrasion-resistant material, with the piston being supported via a roller body, e.g. a ball, on a connection part coupled to a drive device and movably guided in the cylinder transversely to the longitudinal axis. A dry running split-ring seal which permits a predetermined leakage flow of the compressed medium is achieved through the known embodiment in particular for short-stroke small compressors. For this the abrasion-resistant materials of the piston and of the cylinder must be chosen in such a manner that they have at least approximately the same coefficient of thermal expansion in order to keep the leakage loss substantially constant during operation.